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arxiv: 1503.03919 · v1 · pith:LXODWAP2new · submitted 2015-03-13 · 🧮 math.GR · math.LO

An example of a non non-archimedean Polish group with ample generics

classification 🧮 math.GR math.LO
keywords polishamplegenericsgroupnon-archimedeananalyticcorrespondingexample
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For an analytic $P$-ideal $I$, $S_I$ is the Polish group of all the permutations of $\mathbb{N}$ whose support is in $I$, with Polish topology given by the corresponding submeasure on $I$. We show that if $\mbox{Fin} \subsetneq I$, then $S_I$ has ample generics. This implies that there exists a non non-archimedean Polish group with ample generics.

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